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3
votes
0
answers
100
views
good choice of extension of equivariant map
By equivariant obstruction theory, each $K-$map $$f: H\longrightarrow Y$$ can be extended to a $K-$map $$\widetilde{f}: G\longrightarrow Y$$ which is unique up to homotopy rel $H$. …
3
votes
1
answer
142
views
What's the topology on the mapping space $Map_H(G, Y)$ when $G$ is not finite
When $G$ is a finite group and $H$ a closed subgroup of it, the sets of right cosets $H\backslash G$ has the discrete topology on it. Let $Y$ be a $H-$space. We have the $G-$homeomorphism \begin{equa …
2
votes
1
answer
249
views
How to extend an equivariant map from a compact Lie group
All the equivariant properties of the maps in $Map_{C_G(g)}(G, Y)$ are satisfied if and only if the image of each $\alpha$ is in $Y^{\alpha H\alpha^{-1}\cap C_G(g)}$. …